The presence of a more distant object helps judge an object's position in depth. To find out why, we examined whether misjudging a distant cube's location induces a corresponding misjudgment of a nearer sphere's location. Various configurations of a distant cube and a near sphere were presented in total darkness. Each configuration was presented twice: in one presentation, subjects localized the sphere with their unseen index finger, and in the other presentation, they localized the cube in the same way. Three cube sizes were used. Most subjects judged a larger cube to be nearer than a smaller one that was at the same position. For about half of the subjects, cube size had a significantly smaller effect on the judged distance of the sphere in terms of target vergence. Thus, the distance between the judged positions of the two objects was inconsistent with the relative disparity between them. This contradicts claims that the furthest object is localized and used as an anchor point for distance judgments based on correctly perceived relative disparity.

*pointing*. The object that subjects were to point at could either be the sphere or the cube. They started each pointing movement with their right hand near their body. When the target appeared, they moved their unseen index finger to where they saw the target and held the finger steady until the trial ended with the target disappearing. At that moment, the finger position was recorded. The trial ended if the hand was within 30 cm of the center of the volume of possible cube positions and had not moved more than 1 mm in 300 ms. After the target disappeared, the subjects had to bring the hand back near to their body and wait until a new target appeared at another location.

*t*-tests. A similar analysis was conducted for the influence of the cube's angular size on the pointing distance when pointing at the cube, although it is important to realize when interpreting the results of this analysis that the cube's angular size is not independent of its distance.

*t*-tests across the 60 matched pairs of object positions). For each subject, we also averaged the differences between the indicated cube positions and those between the indicated sphere positions, across all 60 pairs of object positions (and determined the corresponding standard errors).

*p*< 0.001). The sphere's angular size did not have a systematic effect on the pointing distance (mean slope: −7.5 cm/deg;

*p*= 0.36). Subjects also pointed further away when pointing at more distant cubes (mean slope: 0.44;

*p*< 0.05) as well as when pointing at smaller cubes (mean slope: −42.5 cm/deg;

*p*< 0.05). Figure 3 shows raw pointing data for two subjects, both for pointing at the sphere and for pointing at the cube. For subject A, the cube's size influenced its judged position in depth: for the same simulated cube position in depth, the subject pointed nearer for the 12-mm cube than for the 8-mm cube, and nearer still for the 16-mm cube (the blue curves are clearly separated). There was no corresponding effect of distant cube size when pointing at the sphere (the green curves are on top of each other), contrary to the prediction of the anchoring hypothesis. For subject B, the cube's size had little effect on the pointed position in depth when pointing at the cube (the blue curves are on top of each other). The same lack of effect of cube size is seen for pointing at the sphere (the green curves are also on top of each other) in accordance with the anchoring hypothesis.

*anchoring hypothesis*, the points should be located along the diagonal line that corresponds to relative disparity being judged correctly (same cube size effect for pointing at the sphere as for pointing at the cube). Most points lie below the diagonal line. For 8 subjects, the effect of cube size on pointing at the distant cube is significantly larger than its effect on pointing at the nearer sphere. Thus, about half of the subjects misjudge the positions in a manner that is inconsistent with judging the sphere's position from a combination of the cube's apparent position and the (correctly perceived) relative disparity. Their data are therefore inconsistent with the

*anchoring hypothesis*.

*limiting factor hypothesis*. The same relative disparity can arise from many different pairs of object positions in depth. Given a value of relative disparity (

*α*), and considering that the furthest possible position of the farther object of the pair of objects is infinitely far away, which corresponds to parallel lines of sight, there is a geometric limit to the possible positions in depth of the nearer object of the pair (shown by the dark red point in Figure 5). Therefore, the presence of the farther object reduces the range of possible positions of the nearer one without the farther object having to be localized. Similar reasoning can be applied to other distances than infinitely far away when one is within an enclosed environment, where the farther object can be assumed not to be further away than a certain distance (e.g., the estimated distance to the wall).

*anchoring hypothesis*in its original formulation by Blank (1958) is rejected by the critical finding that the perceived positions do not comply with the relative disparities.